A press nut to engage with threads of a bolt when it is pressed onto the bolt so as to receive the bolt in its inserting hole is disclosed, for example, in Japanese Patent Publication No. 6-81830. The press nut described in this publication has an outer shell in a nut-like external form having a tapered inner wall whose inner diameter is gradually reduced toward an opening on an end, a plurality of split nuts which have tapered outer surfaces along the tapered inner wall of the shell and are formed with the threaded grooves on their center side inner walls, and coil springs to push up the split nuts to the tapered inner wall of the shell. As this press nut engages with threads of the bolt when it is pressed onto the bolt so as to receive the bolt in its inserting hole, strongly pressing the nut on the bolt moves the nut directly to a clamping position and so it does not require operation to rotate it to the clamping position, which is necessary for prior nuts. A press nut that is similar to the one described in the above publication is shown in FIGS. 7 and 8 and related description of Japanese Patent Publication No. 6-147214. It does not need rotating operation either.